2 Yea, I make a record in the language of my father, which consists of the learning of the Jews and the language of the Egyptians. (1 Nephi 1)
Perhaps on a surface level, this statement might seem implausible to a modern reader, which is why I titled the post the way I did.
Nephi was neither a Jew nor an Egyptian. He descended from one of the Northern Ten Tribes of Israel, and his family presumably fled to Jerusalem around the time of the Assyrian conquest of the Kingdom of Israel a generation of two before Lehi. It is most likely that they were well-to-do refugees, given that they had lands of inheritance separate from Jerusalem.
We learn in Alma 10:3 that Lehi descended from Manasseh, one of the sons of Joseph, so the historical Egyptian tie-in is pretty obvious. I could easily envision the Northern Tribes as having retained a tradition that was much more influenced by Joseph and Egypt than the southern Kingdom of Judah. This could have easily included a writing system. This would be similar to how my Anglo-Saxon ancestors never considered themselves Romans, and yet they readily adopted the Roman alphabet so long ago that we don't often stop to consider its origin.
It is also nearly certain that Nephi had some formal training in a scribal tradition. He displays a high degree of skill in Hebrew rhetoric and a very advanced knowledge of the scriptures. The learning of the Jews makes sense, too, because if Lehi's family was living in Jerusalem, the formal scribal traditions would have been heavily influenced by Judah. I could also imagine that Nephi and his brothers grew up speaking the Judah dialect of Hebrew on the streets but a somewhat different version of a Hebrew-like language in his home, similar to the differences between British English and American English.
I was pretty old when I first came to understand how different the history of spoken language is from the history of written language. Joseph Smith, if he were the author of the Book of Mormon, would have needed a clear understanding of this distinction -- not to mention a clear understanding of the history of the conquest(s) of various ancient Palestinian kingdoms and the resulting refugee crises -- in order to weave this into the story.